Firstly, you have to ensure that you're in a pitch black room, or outside at night time. However, as you set things up, you can have your light on if you're inside. I used my bedroom for the shot above, but I recommend going outside, as you have a lot more room to use.
After you're in a pitch black area with plenty of room, set up your tri-pod and camera, (or use a wall or desk to put your camera on.) Then, you have to switch your focus to Manual because it'll be way too dark for your camera to focus when you do the photo.
If you're inside, turn the room light on and focus on the wall, which you'll be standing in front of when you paint with light. If you are outside, place a torch or some sort of light on the ground and focus on that, but make sure you stand in line with it when you paint, so that your light is in focus.
Next, download an app on your smartphone called SpriteBrush. It's free on Android, (I'm not sure about iOS, but if you search 'photography strobe' or 'light painting' in the app store, you'll find apps that do the trick.) This app may look quite weird, as you can see from the image below, but SpriteBrush is the best for light painting.
Now you've got the app, set up your camera. My recommended exposure settings are: shutter-speed 10secs – 30secs; aperture f/11; ISO 100. To be honest, the shutter-speed can't be set in stone because you'll find that you have to play around with it, depending on how much light you're using.
Also on your camera, link up a shutter release or alternatively, set the self-timer to 10 seconds, so that you have enough time to walk back from the camera and get in position, as well as prepare the light you're going to use on your app.
Your White Balance should be Fluorescent, as it should always be when you're only using florescent or LCD lighting. To boost the colour of your light painting, go to the menu and into Picture Style (with Canon), and then increase both the Saturation and Colour Tone dial to full.
Now that you're all set up, play around with the app and take a few shots. To get the swirling lights flying all the place, just move the phone around in random, swirling ways, as if it's dancing in the sky. The more random the better. And if you're outside, don't be afraid to walk around with the phone, as long as you stay in the frame, of course.
You'll probably end up spending about an hour taking lots of shots, or at least you should. After that, if you have the photo you wanted , then that's great. If you didn't get a photo like mine, don't panic! You can use Photoshop to help, like I did.
What I did in Photoshop is merge all of my favourite photos together, to make one colourful creation that's more pleasing to the eye.
To do this, open up your favourite photos into Photoshop and then layer them on top of each other. Then change the Blending Mode of each layer to Lighten, except the bottom one. This will only show the light parts of each layer on the one below, creating a merge of all the light you created.
Finally, use Levels or Curves to darken the shadows, ensuring that all dark parts of the photo are black. To help with colour, feel free to mess around with Hue/Saturation to both change and boost the overall colour.